Question

(Cos2пи/9*ctg^2пи/9 + sin2пи/9*ctgпи/9)*tg^2пи/9

Answer 1

$(cos \frac{2 \pi }{9}* ctg^{2} \frac{ \pi }{9} +sin \frac{ 2\pi }{9} *ctg \frac{ \pi }{9} ) tg^{2} \frac{ \pi }{9}=$$cos \frac{2 \pi }{9} * ctg^{2} \frac{ \pi }{9} * tg^{2} \frac{ \pi }{9}+sin \frac{2 \pi }{9}*ctg \frac{ \pi }{9} * tg^{2} \frac{ \pi }{9} =cos \frac{2 \pi }{9}$$+sin \frac{2 \pi }{9} *tg \frac{ \pi }{9}=cos \frac{2 \pi }{9} +2sin \frac{ \pi }{9}*cos \frac{ \pi }{9} *tg \frac{ \pi }{9} =$$cos \frac{2 \pi }{9} +2sin \frac{ \pi }{9} *sin \frac{ \pi }{9} = cos^{2} \frac{ \pi }{9} - sin^{2} \frac{ \pi }{9}+2 sin^{2} \frac{ \pi }{9}=$$cos^{2} \frac{ \pi }{9} + sin^{2} \frac{ \pi }{9} =1$